The present invention claims priority to Japanese Patent Application No. 2002-282167, filed Sep. 27, 2002, which is herein incorporated by reference.
1. Field of the Invention
The present invention generally relates to estimating meteorological quantities and, more particularly, to estimating meteorological quantities based on a meteorological time-series model.
2. Discussion of Background
As a derivative product for hedging reduction of sales amount and increase of cost resulting from variations of temperature, amount of rainfall and amount of snow coverage or the like, a weather derivative (transaction) is known. The weather derivative transaction is agreed between customers (enterprises, organizations, corporate organizations and associations, etc.) whose amount of sales is largely affected by weather conditions and, for example, product-liability insurance companies (banks, etc.). In the case of hedging the risk for reduction of sales amount because of a lower temperature in comparison with normal years, a customer and a product-liability insurance company agreed, for example, in the contract of following contents for the purpose of weather derivative transactions
(1) Observation period: from June 1st to August 31st
(2) Weather index: Average temperature (the number of days in which the average temperature of a day is less than 25xc2x0 C.)
(3) Observation point: Tokyo
(4) Strike value: Four days (Compensatory payment may be received from a 5th day in the case where there are four or more days when the average temperature of a day is less than 25xc2x0 C.)
(5) Compensatory payment: $10 per day (upper limit: $200)
(6) Premium: $50
When the weather derivative transaction of the contract content described above is executed, the amount of compensatory payment is different depending on estimation of weather index within the observation period. Therefore, estimation of weather index is very important for both the customer and the product-liability insurance company.
For estimation of meteorological quantities such as temperature and amount of rainfall, etc. as the weather index, a method has been introduced in which a meteorological time-series model has been formed first from historical data of meteorological quantities in the past at the observation point. Then fluctuation of meteorological quantities within the observation period has been estimated with the Monte-Carlo simulation based on this model.
As an example, we will explain the Dischel model which is famous as a weather time-series model for temperature of each day. The Dischel model is expressed by the Formula 1:                                                                         T                n                            =                                                                    (                                          1                      -                      β                                        )                                    ⁢                                      xe2x80x83                                    ⁢                                      Θ                    n                                                  +                                  β                  ⁢                                      xe2x80x83                                    ⁢                                      T                                          n                      -                      1                                                                      +                                  ϵ                  n                                                                                                                        xe2x80x83                            ⁢                                                ϵ                  n                                ∼                                  Normal                  ⁡                                      [                                          μ                      ,                                              xe2x80x83                                            ⁢                                              σ                        2                                                              ]                                                                                                          [                  Expression          ⁢                      xe2x80x83                    ⁢          1                ]            
Here, n represents the n-th day (for example, Feb. 1, 2000 when n=32) in the case where the desired day (for example, Jan. 1, 2000) is defined as the first day, "THgr"n represents the average temperature of the date corresponding to the n-th day (average temperature of several years in the past of the February 1 when n=32, for example), Tn represents the temperature of the n-th day. Here, the parameters xcex2, xcexc, "sgr" are constants. Moreover, xcex5n is a stochastic variable which follows the normal distribution of average xcexc and variation "sgr"2. In addition, xcex2 indicates a rate of dependence of temperature Tn of the n-th day respectively on the average temperature "THgr"n of several years in the past of the object day and the temperature Tnxe2x88x921 of the yesterday of the object day n. Values of three parameters are generally estimated using the least-squares method from the historical data of temperature of several years in the past at the observation point.
When the parameters are once determined, temperature time-series sequence T1, T2, T3, . . . can be sequentially estimated by giving the initial value T0 and random number sequences xcex51, xcex52, xcex53 . . . . When the estimation period is ranged from n=1 to n=N, a set of estimated temperature time-series sequences is formed of T1, . . . , TN. Such estimated temperature time-series sequences are estimated from several thousands to several tens of thousands examples by changing the random number sequences.
An amount of compensatory payment to be paid to a customer from the product-liability insurance company is calculated in each estimated time-series sequence in order to calculate probability density distribution. The product-liability insurance company finally calculates a premium based on this probability density distribution. The premium calculation process has been summarized above.
Moreover, estimation of meteorological quantities such as temperature and amount of rainfall has very important significance for company strategy, completion of various events and activities. In addition, everyone is interested in the matters represented by meteorological quantities such as temperature and amount of rainfall.
A meteorological model used in the economic activities represented by weather derivative transaction is a simplified time-series model where attention is paid only to meteorological fluctuation at a spatial point, namely at the observation point. When parameters of the model are estimated only from the historical data of meteorological quantities, future forecast using a model only indicates an average tendency at the observation point. In other words, practical tendency of each year that it is likely to be cool this summer cannot be estimated.
Such detail estimation of meteorological phenomenon is always requested to introduce a large amount of processes and advanced skill to evaluate various data such as execution of simulation in the global scale based on the extremely detail meteorological mechanical model which has been done by the Meteorological Agency.
Actually, the Meteorological Agency announces long-range weather forecast data of the next one months and three months for temperature and amount of rainfall based on the references such as result of large scale simulation. The long-range forecasts are issued in three grades that the average temperature in the forecast period (amount of rainfall in the forecast period) is xe2x80x9cbelow-normalxe2x80x9d, xe2x80x9cnear-normalxe2x80x9d and xe2x80x9cabove-normalxe2x80x9d. The range of each grade is defined to provide equal appearance ratio (33%, respectively) during past 30 years. For example, in the one-month forecast (weather forecast for the period up to September 16 from August 17) of xe2x80x9cKanto and Koshinetsu Regionsxe2x80x9d, an average temperature of the coming month is that xe2x80x9cprobability for below-normal is 20%, probability for near-normal is 50% and probability for above-normal is 30%xe2x80x9d. Accuracy of the long-range weather forecast is improved from year to year and this improvement is expected more and more in future with improvement in capability of computer system.
However, such long-range weather forecast provides only macroscopic information such as probability distribution of average temperature and amount of rainfall during the forecast period. Meanwhile, microscopic information such as probability distribution of temperature and amount of rainfall of each day is often requested for the economic activities represented by weather derivative transaction. In actuality, a meteorological time-series model such as Dischel model has a demerit that tendency of each year cannot be forecasted while it has a merit that microscopic information such as probability distribution of temperature and amount of rainfall of each day can be treated. Therefore, such a meteorological time-series model is considered to have been widely spread in the weather derivative transaction because of the merit described above.
It is important to note that an ideal meteorological times-series model having the merits of both macroscopic and microscopic information can be formed by reflecting the long-range weather forecast providing macroscopic information on the weather time-series model providing microscopic information.
Accordingly, an object of the present invention is to provide a method, a system, a program, and a computer-readable medium for estimating meteorological quantities of each day reflecting the long-range weather forecast announced by the Meteorological Agency in order to accurately evaluate adverse effect of the meteorological quantities such as daily temperature and amount of rainfall on the economic activities.
In view of solving the problems described above, in one example, a method is provided for estimating meteorological quantities. The method comprises acquiring estimation conditions for meteorological quantities including historical data of meteorological quantities such as temperature and amount of rainfall observed in the past; acquiring an estimation period for estimating meteorological quantities at an estimation point; acquiring a number of times for a simulation; acquiring long-range weather forecast data provided by the Meteorological Agency for the meteorological quantities during the estimation period at the estimation point; creating a meteorological time-series model for the meteorological quantities during the estimation period at the estimation point based on acquired historical data of meteorological quantities and acquired long-range weather forecast data; conducting for the number of times the simulation using the meteorological time-series model; and outputting a meteorological quantities estimation result based on the simulation using the meteorological time-series model.
The invention encompasses other embodiments of a method, a system, an apparatus, and a computer-readable medium, which are configured as set forth above and with other features and alternatives.